Direct intermolecular contacts

The biochemical studies [2,7] showed that the complexes with only the protein or only the DNA mutated exhibit lower binding affinity. On the atomic level of the molecular dynamics simulations this fact should result in overall fewer intermolecular contacts in the ``wrong'' complexes.

This conclusion is readily supported by Figure 3.4, which presents the time dependence of the number of direct hydrogen bonds between Gln (or Lys) 50 and Asn51 and five base pairs of the DNA (CCATT or GGATT) as well as the time dependence of the number of hydrophobic contacts between the four side chains of the recognition helix and the five base pairs. A hydrogen bond was defined as a distance between two heavy hydrogen bonding atoms (nitrogen or oxygen) shorter than 3 Å. A hydrophobic contact was defined as a distance between any other pair of heavy atoms, shorter than 4.5 Å.

  

Figure 3.4: Direct hydrogen bonds (left) and hydrophobic contacts (right) in the four complexes.

 

Table 3.1: The average number of intermolecular hydrogen bonds and hydrophobic contacts. Contacts in the four complexes over the lapse of molecular dynamics simulations, formed by residues 47, 50, 51 and 54, and the base pairs 6-10. Note that the numbers for the double mutant are obtained from the first 160 ps of the run. The end of the run was discarded, as described in the section on RMSD test.

	average # of h-bonds	average # of hydrophobic contacts
wild type	$1.0 \pm 0.7$	$27 \pm 6$
protein mutant	$0.6 \pm 0.8$	$20 \pm 6$
DNA mutant	$0.2 \pm 0.4$	$14 \pm 4$
double mutant (160 ps)	$1.5 \pm 1.0$	$30 \pm 5$

 

Figure 3.4 is summarized by Table 3.1, which presents the average number of contacts per snapshot for the four parallel runs. One can conclude that the complexes with only one mutation (in the polypeptide or in the DNA) have fewer direct intermolecular contacts than the wild type complex. The doubly mutated complex, on the other hand, forms even more contacts to the DNA, which agrees with the biochemical result, that the double mutant showed greater binding affinity than the wild type complex.

  

Figure 3.5: Direct hydrogen bonds (left) and hydrophobic contacts (right) formed by residue 50.

A similar trend is present in the contacts made by residue 50 of the polypeptide, which is the site of the mutation, and which is responsible for specific recognition. Figure 3.5 and Table 3.2 indicate that Lys50 in the complex with the mutated protein forms almost no direct contacts to the DNA. Lys50 of the double mutant, on the contrary, forms more contacts than Gln50 in the wild type complex.

 

Table 3.2: The average number of intermolecular hydrogen bonds and hydrophobic contacts formed by residue 50. Note, that an average of 0.0 with a certain deviation results from very few contacts during the run with possibly a larger number of contacts during a short period, which contribute to increase in deviation.

	average # of h-bonds	average # of hydrophobic contacts
wild type	$0.9 \pm 0.6$	$8.5 \pm 2.5$
protein mutant	$0.0 \pm 0.3$	$1.9 \pm 4.8$
DNA mutant	$0.2 \pm 0.4$	$6.3 \pm 2.1$
double mutant (160 ps)	$1.4 \pm 0.9$	$10.8 \pm 3.2$

 

The mutations Gln50$\to$Lys in the protein and C6C7$\to$GG in the DNA, certainly lead to different patterns of direct intermolecular contacts in the immediate neighbourhood of the mutation sites. However, the results of the molecular dynamics simulations suggest that differences appear even in more remote places. An occasion of such event is the behaviour of Asn51, which is a strictly conserved residue over all homeodomains, in the four complexes.

  

Figure 3.6: Direct hydrogen bonds (left) and hydrophobic contacts (right) formed by Asn51.

As one can see from Figure 3.6 and Table 3.3, Asn51 in the complex with the mutated protein forms significantly more contacts than in the other three systems. It should be noted in this respect, that after about 50 ps of the run, the recognition helix deformed at residue 51. This deformation was followed by Asn51 contacting base pair 9 (TAATGG of the $\beta$-strand) (see Figure 3.7). There is no similar phenomenon of a recognition helix distortion in the other runs.

 

Table 3.3: The average number of intermolecular hydrogen bonds and hydrophobic contacts formed by Asn51.

	average # of h-bonds	average # of hydrophobic contacts
wild type	$0.2 \pm 0.4$	$4.4 \pm 2.1$
protein mutant	$0.6 \pm 0.8$	$9.3 \pm 5.3$
DNA mutant	$0.0 \pm 0.1$	$2.8 \pm 1.8$
double mutant (160 ps)	$0.1 \pm 0.3$	$4.6 \pm 2.2$

 

  

Figure 3.7: Time development of the backbone and side chain angles of residue 51 in the complex with protein mutant (left). The time axis is represented by the radius of the circle; the angles are counted from the dashed line, the clockwise direction being positive. Time dependence of the distances between Asn51 and base pairs 9 and 10 (right), the only ones formed by Asn51 in the protein mutant complex.

According to these simulations, Ile47 forms most contacts in the wild type complex, whereas Met54 has most contacts in the doubly mutated system. The results are presented in Figure 3.8.

  

Figure 3.8: Number of hydrophobic contacs formed by Ile47 and Met54 in the four complexes. Ile47 (left) forms most contacts in the wild type complex, whereas Met54 (right) in the double mutant. It forms least contacts in the wild type system.

Still one more test to cast light on the binding specificity is to compare the number of contacts residue 50 forms to base pairs 6 and 7. These numbers (see Table 3.4) reveal that base pair 7 is contacted more often in the ``correct'' complexes, whereas base pair 6 forms more contacts to Gln50 than to Lys50. In the ``wrong'' systems, moreover, both base pairs form approximately the same number number of contacts to residue 50.

 

Table 3.4: The average number of direct contacts formed by residue 50 to base pairs 6 and 7 in the four runs.

	hydrogen bonds
	base pair 6	base pair 7
wild type	0.3	1.4
protein mutant	0.1	0.1
DNA mutant	0.7	0.7
double mutant (160 ps)	0.1	1.6
	hydrophobic contacts
	base pair 6	base pair 7
wild type	1.6	5.7
protein mutant	1.0	0.8
DNA mutant	3.7	2.5
double mutant (160 ps)	0.5	5.4

 

As an overall conclusion from the analysis of the direct contacts one could state that the wild type and doubly mutated complexes show greater binding affinity than the complexes with only one mutation. This agrees with the biochemical analysis of the systems [7]. According to the above results, residue 50 is mostly responsible for such specificity, although Ile47 in the wild type system and Met54 in the double mutant complex significantly add to the number of direct contacts and contribute to the increase in binding affinity. Asn51, on the other hand, does not fall in this description--it assures certain affinity to the complex with the mutant protein by forming significantly more contacts in it compared to the other three systems. One can also state that base pair 7 is more important in recognition, since it forms more contacts to residue 50, than base pair 6.